Kevin Reza took second while Michal Kwiatkowski extended his streak of third-place finishes to three.
Alberto Contador enjoyed a comfortable day in the peloton and maintained his 14 second advantage over Alejandro Valverde.
Although an early breakaway headed by Andy Schleck was quickly reeled in by the peloton, the pack were content to permit Ruben Fernandez’s solo escape after 40 kilometres.
But despite amassing a lead of eight minutes, the stage eventually took its toll and the lead shrunk – the Spaniard’s hopes of victory ending on the Gasteiz climb.
A chaotic sprint ensued with a host of riders battling for position before Matthews latched onto the back wheel of Gerrans and sprinted to victory.
Stage three results
1. Michael Matthews (Australia / Orica) 5:02:09"
2. Kevin Reza (France / Europcar) ST
3. Michal Kwiatkowski (Poland / Omega Pharma - Quick-Step)
4. Ben Swift (Britain / Team Sky)
5. Paul Martens (Germany / Belkin)
6. Yukiya Arashiro (Japan / Europcar)
7. Daniele Ratto (Italy / Cannondale)
8. Maxim Iglinskiy (Kazakhstan / Astana)
9. Enrico Gasparotto (Italy / Astana)
10. Tosh Van der Sande (Belgium / Lotto)
1. Alberto Contador (Spain / Tinkoff - Saxo) 12:54:03"
2. Alejandro Valverde (Spain / Movistar) +14"
3. Michal Kwiatkowski (Poland / Omega Pharma - Quick-Step) +34"
4. Damiano Cunego (Italy / Lampre) +36"
5. Cadel Evans (Australia / BMC Racing)
6. Jean-Christophe Peraud (France / AG2R)
7. Yury Trofimov (Russia / Katusha)
8. Mikel Nieve (Spain / Team Sky)
9. Roman Kreuziger (Czech Republic / Tinkoff - Saxo) +54"
10. Mikel Landa (Spain / Astana)
- Sports & Recreation
- Alberto Contador
- Michal Kwiatkowski
- Alejandro Valverde
- Andy Schleck
- Michael Matthews